Question: Given $ m \angle AOB = 3x + 19$, $ m \angle BOC = 9x - 33$, and $ m \angle AOC = 82$, find $m\angle AOB$. $O$ $A$ $C$ $B$
Answer: From the diagram, we see that together ${\angle AOB}$ and ${\angle BOC}$ form ${\angle AOC}$ , so $ {m\angle AOB} + {m\angle BOC} = {m\angle AOC}$ Substitute in the expressions that were given for each measure: $ {3x + 19} + {9x - 33} = {82}$ Combine like terms: $ 12x - 14 = 82$ Add $14$ to both sides: $ 12x = 96$ Divide both sides by $12$ to find $x$ $ x = 8$ Substitute $8$ for $x$ in the expression that was given for $m\angle AOB$ $ m\angle AOB = 3({8}) + 19$ Simplify: $ {m\angle AOB = 24 + 19}$ So ${m\angle AOB = 43}$.